It looks like "smallexample" class is used for all? code blocks in the
manual.

We also have an emacs specific manual.css:
https://www.gnu.org/software/emacs/manual.css

I also quickly looked through https://www.gnu.org/combo.css and
https://www.gnu.org/layout.css but didn't find anything related to
"smallexample".

But I don't know enough css to say how the smallexample class should be
formatted so that it looks good on any browser/screen. Hopefully someone
with a know-how on this topic can chime in.